Chucklevision was quite different in its early days...
Indeed it was, and as mentioned, the reason it was called Chucklevision was because it was about the pair running a TV station and it was mostly studio-bound, which is an idea that went out of the window after the second series. The story in the middle then spun off into a series of its own called Mersey Tales, which was actually shown on the same day as the third series of Chucklevision -
https://genome.ch.bbc.co.uk/schedules/bbcone/london/1989-12-02#at-8.00
Of course it was originally a BBC Manchester production and was one of the few shows to survive their children's department closing down in the early nineties. Why Don't You and Activ8 also continued, now made out of London (and the latter then moved to Glasgow) but clearly Chucklevision was the last legacy of that department, by several years.
Nobody's mentioned my favourite episode of Chucklevision, which was the one guest starring Roy Castle where they tried to get in the Guinness Book of Records, and Barry sang Doin' The Do at him for 24 hours. That one's not on YouTube anymore, alas.
Run The Risk was effectively Double Dare in new packaging. DD finished in 1992 and Risk started six months or so later. I'm not entirely sure why it happened the way it did, though Risk was probably more original then Dare, which itself was an imported format from America. I dare say most people remember moments from both shows interchangeably.
Double Dare was getting on a bit as well, they started tinkering with the format and then for half a series it was replaced by Clockwise which had moved from the afternoon. Was it on here where someone suggested that Get Your Own Back had originally been intended for a slot on Going Live as well? That would make sense, it clearly had a similar budget and looked quite similar. So seemingly they were trying other things out.
As you say, Double Dare was an acquired format so presumably one reason for replacing it with Run The Risk was because it was a wholly-owned BBC format which they could exploit as they saw fit and not pay licencing fees.
Initially Double Dare played a really pivotal role in Going Live, Peter Simon was in the Going Live studio every week doing bits and bobs, as well as introducing Saturday Starts Here as mentioned, and the two shows' sets looked very similar and they presented it as if Double Dare was live. Later on Double Dare became just another insert and they rarely mentioned it on the rest of the show, and Peter Simon was hardly ever live.